$J$ is the midpoint of $\overline{CT}$ $C$ $J$ $T$ If: $ CJ = 9x + 3$ and $ JT = 8x + 10$ Find $CT$.
Solution: A midpoint divides a segment into two segments with equal lengths. ${CJ} = {JT}$ Substitute in the expressions that were given for each length: $ {9x + 3} = {8x + 10}$ Solve for $x$ $ x = 7$ Substitute $7$ for $x$ in the expressions that were given for $CJ$ and $JT$ $ CJ = 9({7}) + 3$ $ JT = 8({7}) + 10$ $ CJ = 63 + 3$ $ JT = 56 + 10$ $ CJ = 66$ $ JT = 66$ To find the length $CT$ , add the lengths ${CJ}$ and ${JT}$ $ CT = {CJ} + {JT}$ $ CT = {66} + {66}$ $ CT = 132$